Finite Group Databasebeta

← #21455875

Subgroups — #21455875

Order 7808.

434 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic, complemented
2C4×#11758224C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840085C211yesmaximal, characteristic, complemented
5#16840056C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16839961C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839908C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11C4×#11758190C211yesmaximal, characteristic, complemented
12C4×#11758200C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C4×D8×C61C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758224C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519763—21no—
24#14519752C2211yescharacteristic
25#14519750—21no—
26#14519748C2211yescharacteristic
27C4×Dic122C2211yescharacteristic
28#14519742C2211yescharacteristic
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31C4×C22⋊D61—21no—
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519733—21no—
36C2×C4×Dic61—21no—
37C42×D61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758224—22no—
70#11758224—22no—
71#11758222—44no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61D411yescharacteristic
76C2×C4×D61D411yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79C2×Dic122C2311yescharacteristic
80D8×C61—22no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200—22no—
91#11758199—22no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61D411yescharacteristic
104C4×Dic61D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109C23×C61—21no—
110C23×C61—21no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113D4×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61#4112yescomplemented
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—24no—
125C22⋊D61—42no—
126C22⋊D61—42no—
127C22⋊D61—42no—
128C2×Dic61—24no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—21no—
137D244—21no—
138D244—42no—
139C4×D61—22no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—22no—
143C4×D61—42no—
144Dic122—21no—
145Dic122—42no—
146Dic122#4112yescomplemented
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61AGL(1,ℤ/8)12yes—
168C4×C61C2×#4111yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61#13512yes—
176#3106—611nomaximal, Sylow
177C2×C61—42no—
178C2×C61—81no—
179C2×C61#52511yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
182D61—41no—
183D61—81no—
184#532—611no—
185C4×#41—611no—
186#482—611no—
187#482—611no—
188#477—611no—
189#476—611no—
190#460—611no—
191#459—611no—
192#449—611no—
193#449—611no—
194C4×SD16—611no—
195C4×SD16—611no—
196C4×D8—611no—
197C4×D8D6111yescharacteristic, complemented
198#431—611no—
199C61#310611yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C2×#41—1221no—
202C2×SD16—611no—
203C2×SD16—611no—
204C2×D8—611no—
205C2×D8C2×D6111yescharacteristic
206C4⋊Q8—611no—
207#127—611no—
208#124—1221no—
209#121—611no—
210#121—611no—
211#121—1221no—
212C4×Q8—611no—
213C4×Q8—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218C4×D4—1221no—
219C4×D4C2×D6111yescharacteristic
220C4×D4C2×D6111yescharacteristic
221#117—611no—
222#117—1221no—
223C2×C42—611no—
224C2×C42—1221no—
225#107—611no—
226#107C2×D6111yescharacteristic
227#106—611no—
228#106—611no—
229C4⋊C8—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237#102C2×D6111yescharacteristic
238#102C2×D6111yescharacteristic
239C22⋊C8—611no—
240C22⋊C8—611no—
241C4×C8—611no—
242C4×C8C2×D6111yescharacteristic
243#41—1222no—
244#41—1222no—
245#41—2444no—
246C2×Q8—611no—
247C2×Q8—1221no—
248C2×D4—611no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4C22×D6111yescharacteristic
255C2×D4C22×D6111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264SD16—1222no—
265SD16—1222no—
266D8—22no—
267D8—1222no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—611no—
287C42—611no—
288C42—611no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C42C22×D6111yescharacteristic
293C23—21no—
294C23—21no—
295C23—611no—
296C23—1221no—
297Q8—612no—
298Q8—1221no—
299Q8—2442no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—1224no—
304D4—1221no—
305D4—1221no—
306D4—2442no—
307D4—2442no—
308D4—2442no—
309D4—2442no—
310D4#1175822212yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1224no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1222no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4D4×D6111yescharacteristic
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—21no—
332C8—21no—
333C8—1221no—
334C8—1221no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—612no—
352C4—1221no—
353C4—1222no—
354C4—1221no—
355C4—2441no—
356C4—2441no—
357C4#1451980112yes—
358C4#41×D6111yescharacteristic
359C4C2×#1175822211yescharacteristic
360C2—42no—
361C2—81no—
362C2—4881no—
363C2—2441no—
364C2#1684027111yescharacteristic
365C2#135×D6111yescharacteristic
366C2C2×#1451980111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×D8×C61C2
socleC22×C61C22×D4
hypercenterC4×D8D61
hypocenterC61#3106
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16840309C2semidirect
2. C4×#11758224C2semidirect
3. #16840089C2semidirect
4. #16840085C2semidirect
5. #16840056C2semidirect
6. #16840050C2semidirect
7. #16839961C2semidirect
8. #16839955C2semidirect
9. #16839908C2semidirect
10. #16839904C2semidirect
11. C4×#11758190C2semidirect
12. C4×#11758200C2semidirect
13. C4×#11758199C2semidirect
14. #16839813C2semidirect
15. C4×D8×C61C2semidirect
116. D4×C61#41semidirect
146. Dic122#41semidirect
197. C4×D8D61semidirect
199. C61#3106semidirect
310. D4#11758222semidirect